A circle is described around the square and a circle is inscribed in the square.

A circle is described around the square and a circle is inscribed in the square. Find the area of a circular ring if the area of the square is 16 cm ^ 2.

Square side a = √S = √16 = 4 (cm)

Radius of the circumscribed circle:

R = a / √2 = 4 / √2 = 2 √2 (cm)

Area of the circumscribed circle

S = P R² = P (2√2) ² = 8 P (cm²)

Inscribed circle radius:

r = a / 2 = 2 (cm);

Inscribed area:

S ‘= P r² = 4 P (cm²);

Ring area

S ” = 8 P – 4 P = 4 P = 12.56 (cm²)